### Abstract

Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. Unfortunately, there are non-trivial gaps in the original description. Besides giving a complete treatment, we also give an alternative to his subdivision method which has some nice properties. Among the tools needed are root-separation bounds and non-trivial applications of Brent's complexity bounds on evaluation of elementary functions using floating point numbers.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Editors | Anon |

Publisher | Publ by ACM |

Pages | 41-48 |

Number of pages | 8 |

ISBN (Print) | 0897916484 |

State | Published - Jan 1 1994 |

Event | Proceedings of the 10th Annual Symposium on Computational Geometry - Stony Brook, NY, USA Duration: Jun 6 1994 → Jun 8 1994 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | Proceedings of the 10th Annual Symposium on Computational Geometry |
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City | Stony Brook, NY, USA |

Period | 6/6/94 → 6/8/94 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Choi, J., Sellen, J., & Yap, C. K. (1994). Approximate Euclidean shortest path in 3-space. In Anon (Ed.),

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 41-48). (Proceedings of the Annual Symposium on Computational Geometry). Publ by ACM.